Thanks to user3281336 who suggested installing .NET 4.5. I downloaded .NET 4.5 at http://www.microsoft.com/en-us/download/details.aspx?id=40779 and installed it.
This fixed the problem. The web site would not throw an exception. If it matters, I was accessing www.dnndev.me which is the "default" web site based on one of the DNN installations.
When searching for solutions to this problem "responders trying to help" sometimes said to re-install .NET 4.0, but in my case I didn't try this because I thought the DNN required this. Later I looked back at my notes on the video (see http://www.dnnsoftware.com/community/learn/video-library/view-video/video/515/view/details/dnn-7-0-installation-part-1-file-system-configuration) and it says that only .NET 4.0 was required.
None-the-less, I'm up and running.